text: It is assumed that the waves are of infinitesimal amplitude and the free surface oscillates around the mean level z = 0. The waves propagate under the action of gravity, with a constant acceleration vector by gravity (pointing downward in the negative z direction). Further the fluid is assumed to be inviscid and incompressible, with a constant mass density. The fluid flow is irrotational. At infinite depth, the fluid is taken to be at rest.
  Now the flow may be represented by a velocity potential φ, satisfying the Laplace equation and
  In order to have non-trivial solutions for this eigenvalue problem, the wave length and wave period may not be chosen arbitrarily, but must satisfy the deep-water dispersion relation:
  with g the acceleration by gravity in (m/s). Within the framework of linear theory, the horizontal and vertical components, ξ and ξ respectively, of the Lagrangian position ξ are
  The horizontal component ū of the Stokes drift velocity is estimated by using a Taylor expansion around x of the Eulerian horizontal velocity component u = ∂ξ / ∂t at the position ξ: